Mathematics: Which function does the graph represent? Of(x) = (x - 2)2 + 3 Of(x) = -(x - 2)2 + 3 Of(x) = (x + 2)2 + 3 O f(x) = -(x + 2)2 + 3

Which function does the graph represent? Of(x)

Ответ:

dedrell16

07.04.2022

Mathematics

The function which represents the graph is:

$y=-\left(x\:-\:2\right)^2+\:3$

Hence, option B is correct.

The graph is also attached.

Step-by-step explanation:

From the graph, it is clear that:

The vertex = (2, 3)

The y-intercept = (0, -1)

Let us check the equation

$y=-\left(x\:-\:2\right)^2+\:3$

Determining the y-intercept:

The value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

substituting x = 0 in teh equation

$y=-\left(x\:-\:2\right)^2+\:3$

$y=-\left(0\:-\:2\right)^2+\:3$

y=-2^2+3

y=-4+3

y=-1

Thus,

The point representing the y-intercept is: (0, -1)

Determining the vertex:

The vertex of an up-down facing parabola of the form ax² + bx + c is:

$x_v=-\frac{b}{2a}$

As the equation is

$y=-\left(x\:-\:2\right)^2+\:3$

Rewriting the equation $y=-\left(x\:-\:2\right)^2+\:3$ in the form ax² + bx + c:

y=-x^2+4x-1

The Parabola params are:

$a=-1,\:b=4,\:c=-1$

Thus,

$x_v=-\frac{b}{2a}$

$x_v=-\frac{4}{2\left(-1\right)}$

x_v=2

Now plug in x_v=2 in the equation to find y_v

y_v=-x^2+4x-1

$\:y_v=-\left(2\right)^2+4\left(2\right)-1$

y_v=-4+8-1

y_v=3

Therefore, the vertex of the equation is: (2, 3)

Hence, the function which represents the graph is:

$y=-\left(x\:-\:2\right)^2+\:3$

Hence, option B is correct.

The graph is also attached.

Which function does the graph represent?

Of(x) = (x - 2)2 + 3
Of(x) = -(x - 2)2 + 3
Of(x) = (x + 2)

0,0(0 оценок)

Which function does the graph represent? Of(x) = (x - 2)2 + 3
Of(x) = -(x - 2)2 + 3
Of(x) = (x + 2)2 + 3
O f(x) = -(x + 2)2 + 3

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question